When public transit works well, you see it more as a network of fixed routes than as catching individual vehicles. You show up at a stop, and the system takes you close to your destination. If you miss a bus/tram/train, the next one is probably not too far behind. If you miss a connection, the system may suggest you another route.
The US is full of medium-density cities that don't work well. Population density is high enough that traffic gets bad if most people drive, but it's simultaneously low enough that public transit is only viable on most popular routes.